A federal judge granted lawyers another extension to try to gather enough support among Ground Zero workers to proceed with an $815 million settlement for their health problems.

Judge Alvin Hellerstein had previously given lawyers until midnight Monday to get 95% of the suing police officers, firefighters and laborers involved in the recovery effort at the World Trade Center site to agree to the terms of the settlement. After that deadline passed, the judge issued an order extending the time another week.

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A man protests against the proposed settlement for Ground Zero workers in March.

It is not the first such extension. The original deadline had been in early September.

Lawyers for the workers have insisted that they could could reach the 95% threshold if given more time. “We’re very confident that we’re going to get the 95%,” Marc J. Bern, a lead lawyer for the workers, said on Monday before a judge issued a gag order in the case.

In a two-page order filed late Tuesday, the judge said a “huge influx of plaintiffs opting into the settlement continues to tax the capacity to process the plaintiffs’ releases and other documents evidencing the plaintiffs’ decision to opt in.”

Yet in an order a day earlier, Judge Hellerstein had already given the lawyers an extra three days to handle the paperwork demands of the case. Tuesday’s order was different in that it also gave the lawyers an additional seven days to try to convince Ground Zero workers to agree to the settlement terms — something they wouldn’t presumably need if they had in fact reached the 95% threshold.

More than 10,000 laborers sued the city and its contractors for failing to adequately protect them when they labored on the pile of debris of the collapsed World Trade Center after the Sept 11, 2001, terrorist attacks. Many workers claim to be suffering illnesses — ranging from asthma to blood cancers — caused by inhaling the toxic dust at the site.

The most seriously ill of the workers have overwhelmingly agreed to take the settlement terms. In that group of more than 4,500 workers, more than 98% have opted into the settlement, according to Bern.

Those with lesser ailments generally have less pressing health and financial needs and have been more resistant to the settlement.